As we demonstrated in the previous section, we can estimate a role of each layer by observing the outputs at each hidden layer.
However, the weakness of the method is that it is unclear whether the large intensity output directly represents the contribution for the estimation and we need to speculate the meaning of each output field.
As for more interpretable tool to observe the internal procedure, we here apply a gradient-weighted class activation mapping (Grad-CAM) [1]}, [2]} to our problem settings.
A Grad-CAM has been widely used on the field of image recognition, thanks to its capability in telling us the region with higher interest for the estimation of the trained model.
Other than the image classification, Jagodinski et al. [3]} has recently demonstrated the ability of the Grad-CAM for the probability estimation of ejection events in a turbulent channel flow.
In our study, the ability of Grad-CAM is demonstrated with canonical regression problems, i.e., \(C_D\)  estimation of a two-dimensional cylinder wake [4]} and experimental data estimation [5]} as shown in figures REF \((a)\)  and \((b)\) .
For the problem setting of experimental data estimation, we particularly choose the machine learned model trained by artificial particle images with data lacked region.
The model is originally trained to estimate the velocity field from lacked artificial particle images of flow around both single and double square cylinders.
For more details on this procedure, we refer readers to Morimoto et al. [5]}.
